Amateur Mathematics

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john

22 Apr, 2018 04:11 AM

Today I happened across a fascinating article about a breakthrough in graph theory in Quanta Magazine:

https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/

… and followed a link in that article to a discovery of a related graph posted by a mathematician named Marijn Heule:

https://polymathprojects.org/2018/04/10/polymath-proposal-finding-simpler-unit-distance-graphs-of-chromatic-number-5/#comment-120318

Dr. Heule posted vertex and edge files for his graph, so I decided to plot and animate them using NodeBox.

There were several small challenges. Heule posted his files in Mathematica and DIMACS formats. Mathematica uses expressions instead of absolute values for its coordinates, e.g. {(7 + Sqrt[33])/12, (Sqrt[3] + Sqrt[11])/12}. In order to convert these into something more NodeBox friendly I created an eval custom node that translates any mathematical expression into a value. You might find this node useful in other projects.

Once I had the coordinates it was fairly easy to plot them. I then created an animation to show that these graphs are composed of unit edges all the same length. The animation starts with 4461 unit line segments stacked in a grid and then morphs them to form the graph.

The attached NodeBox file contains a folder with the custom eval node, the data files, and a NodeBox network. The network file includes one network used to transform the original data into tab separated files, and a second network to plot and animate those files.

NodeBox is a great tool to do amateur mathematics with. Enjoy!

John

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